论文标题
可衡量的谐波热流的可测量半群选择
Measurable Semigroup Selection of the Heat Flow for Harmonic Maps
论文作者
论文摘要
J.-M。 Coron在[5]中证明，从$ m $到$ n $的全球弱解决方案（从非平稳的弱谐波地图开始）在$ M = b^3 $和$ n = s^2 $时并不是唯一的。因此，解决方案图的半群属性一般不存在。本简短的论文使用J. Cardona和L. kapitanski开发的技术来表明在J.-M.显示非唯一性的同一情况下，无限的许多可测量的分数求解了热流。 Coron。
J.-M. Coron proved in [5] that the global weak solutions of the heat flow from $M$ to $N$, starting at non-stationary weakly harmonic maps, are not unique when $M = B^3$ and $N = S^2$. Hence, the semigroup property of the solution map does not hold in general. The present short paper uses the techniques developed by J. Cardona and L. Kapitanski to show the existence of infinitely many measurable semigroups solving the heat flow in the same cases where non-uniqueness was shown by J.-M. Coron.
